Dynamically scoped variables in OCaml

Dynamic binding adds expressiveness; as Luc Moreau emphasized,
it is, when used in moderation, quite useful: for parameterizing a
function deep in the code without changing the interface of all
callers; for propagating the environment information like the current
working directory, printing-depth, etc. Dynamic binding is
inescapable in mobile code or continuation-based web servers. Dynamic
binding, in some restricted form, is already present in OCaml:
exception handlers are dynamically scoped. This message announces the
availability of general dynamic binding. This is joint work with
Chung-chieh Shan and Amr Sabry.

Dynamic binding is implemented as a regular library, dependent
on the delimited continuations library. No changes to the OCaml system
and no code transformations are required; (parts of the) code that do
not use dynamic variables incur no overhead and run at the same speed
as before. Our dynamic variables are mutable; mutations however are
visible only within the scope of the dlet statement where
they occurred. It is also possible to obtain not only the latest
binding to the dynamic variable, but also any of the shadowed
bindings.

Because dynamic binding is implemented in terms of delimited
continuations, the two features harmoniously interact. We can use
dynamic variables in shift-based, cooperative threads, and support partial inheritance of the dynamic environment, with both shared and
thread-private (mutable) dynamic variables.

Version

The current version is 1.1, Apr 10, 2006.

References

dynvar.txt [5K]
The announcement with a few examples
It was originally posted on the caml-list on Mon, 10 Apr 2006 18:25:29 -0700

Resumable exceptions

Resumable exceptions are the strict generalization of regular
exceptions, letting the exception raising form return a value and
so the computation may continue. It's the exception handler that
decides either to abort the exceptional computation or to resume it
with a particular value. Resumable exceptions are made popular by
Common Lisp, where they are widely used. Rainer Joswig's message,
cited below, lists several real-life examples of resumable
exceptions.

We show a conservative and elementary implementation of
resumable exceptions in OCaml: the implementation is a self-contained
100% pure OCaml library; makes no changes to the OCaml system;
supports the existing style of defining exceptions; is compatible with
the ordinary exceptions; works in byte- or natively-compiled code;
uses the most basic facilities of ML and so can easily be translated
to SML.

We impose no extra restrictions on the resumable exception
raising and handling forms. Like with ordinary exceptions, resumable
ones may encapsulate values of arbitrary types; the same exception
handler may process exceptions of many types -- and send resumption
replies of many types. The raise form may appear within
the guarded code at many places; different raise forms
may resume with the values of different types. Furthermore, resumable
exceptions are declared just like the ordinary ones,
with the exception keyword. If
the resumable exception handler never resumes, resumable exceptions
act and feel precisely as the regular ones.

Version

The current version is 1.2, Jun 14, 2006.

References

resumable.txt [7K]
Motivation, design and an example of resumable exceptions
This announcement article was originally posted on the caml-list on Wed, 14 Jun 2006 15:54:03 -0700. This file also includes follow-ups, discussing syntactic sugar and the ways to implement resumable exceptions in a multi-threaded system.

Persistent twice-delimited continuations

The new version of the delimcc library of first-class delimited
continuations for byte-code OCaml now supports serializing and storing
of captured continuations. The stored continuation can be invoked in the
same or a different process running the same executable. The
persistence feature supports process checkpointing, migration -- and
specifically CGI programming on any, unmodified web server,
e.g., Apache. Serialized continuations are twice delimited -- both
in `control' and in `data'; the latter makes them compact and
possible. The delimcc library is a pure library; it makes no
changes to the OCaml system and has no effect on the code that does
not capture delimited continuations.

One may think that making captured continuations persistent is
trivial: after all, OCaml already supports marshaling of values
including closures. If one actually tries to marshal a captured
delimited continuation, one quickly discovers that the naive
marshaling fails with the error on attempting to serialize an abstract
data type. One may even discover that the troublesome abstract data
type is _chan. The captured delimited continuation (a
piece of stack along with administrative data) refers to heap data
structures created by delimcc and other OCaml libraries; some of these
data structures are closures, which contain module's environment and
may refer to standard OCaml functions like prerr. That
function is a closure over the channel stderr, which is
non-serializable. This points out the first problem: if we serialize
all the data reachable from the captured continuation, we may end up
marshaling a large part of the heap and the global environment. This
is not only inefficient but also lethal, as we are liable to
encounter channels and other non-serializable data structures.

There is a more serious problem however. If we serialize all data
reachable from the captured delimited continuation, we also serialize
two pieces of global state used by the delimcc library itself. When
the stored continuation is deserialized, a fresh copy of these global
data is created, referenced from within the restored
continuation. Thus the whole program will have two copies of delimcc
global data: one for use in the main program and one for use by the
deserialized continuation. Although such an isolation may be desirable
in many cases, it is precisely wrong in our case: the captured and the
host continuations do not have the common view of the system and
cannot work together. It may be instructive to contemplate process
checkpointing offered by some operating systems (see also `undump'
typically used by Emacs and TeX). When checkpointing a process, we
wish to save the continuation of the process only (rather than the
continuation of the scheduler that created the process, and the rest of
the OS continuation). We also wish to save data associated with the
process, for example, the process control block and the description of
allocated memory and other resources. Control blocks of all processes
are typically linked in; when saving the control block of one process,
we definitely do not wish to save everything that is reachable from
it. When saving the state of a process in a checkpoint, we do not
usually save the state of the file system -- or even of all files used
by the process. First of all, that is impractical. Mainly, it is
sometimes wrong. For example, a process might write to a log
file, e.g., syslog. We specifically do not wish to save the contents
of the syslog along with the process image. We want the restored
process append to the system log rather than replace it!

Of course resuming a suspended process after modifying its
input files may also be wrong. It is a hard question of what should be
saved by value and what should be saved by reference only. It is clear
however that both mechanisms are needed. The serialization code of the
delimcc library does offer both mechanisms. The inspiration comes from
the fact that OCaml's own marshaling function, when handling closures,
serializes OCaml code by reference. The delimcc library extends this
approach to data. The library supports the registration of data (which
currently must be closures in the old heap) in a global array. When
serializing a continuation, the library traverses it and replaces all
references to registered closures with indices in the global array; we
then invoke OCaml's own serialization routine to marshal the
result. After that, we undo the replacement of closures with
indices. Such value mangling is not without precedent: to detect
sharing, OCaml's own marshaling routine too mangles the input
value. The use of the global array is akin to the implementation of
cross-staged persistence in MetaOCaml.

Version

The current version is 1.7, April 2008.

References

Delimited continuations in OCaml
The description of the delimcc library
The persistent twice-delimited continuations have been demonstrated at the Continuation Fest 2008 (April 13, Tokyo, Japan) and described in the message to the Caml-List posted on Sun, 27 Apr 2008 17:53:36 -0700 (PDT).

Persistent delimited continuations for CGI programming with nested transactions
The salient application of persistent delimited continuations is the library for writing CGI scripts as if they were interactive console applications using read and printf. The above library implements the minimal CGI programming framework with form validation. The library also supports nested transactions. The captured continuations are relatively compact: the essentially empty captured continuation takes 491 bytes when serialized. Serialized continuations of the unoptimized blog application have the typical size of 10K (depending on the size of the posts); bzip can compress them to one third of the original size.

Listing toplevel bindings

We show how to list all top-level bindings defined since the
start of the OCaml toplevel session. We can list the names and the
types of the bindings. We can also print the values of top-level
bindings of a specific type. There is no need to recompile
anything. However, we need the OCaml installation directory with the
object files left after the making of the toplevel. If we are willing
to remake the toplevel, the installation directory is no longer
required.

After the preparation step or the alternative preparation step
described below, we enter or #use, in the toplevel, the
code print-toplevel-bindings.ml. We define a few sample
bindings:

For each binding, its name and type are printed. We see that
the type environment keeps track of all the previous
definitions of a name. Because x was defined twice,
there are two entries in the type environment: x/186
and x/187. The counters are the timestamp.

We can also print the values associated with the bindings of
one particular type, for example, int:

If a variable is defined several times, the top-level value
environment keeps the last associated value, however. The function print_int_toplevel cannot, generally, be polymorphic
-- unless we are willing to assume responsibility that our type
representation string matches the desired type -- or we are willing
to use MetaOCaml.

Preparation step
This step requires the OCaml installation directory with the object files left after the building of the toplevel. First, we need to retrieve
gprint_toplevel.ml [2K]
and adjust the paths in the #directory directives to point to our OCaml installation directory. We start the OCaml toplevel and execute all #directory and the #load directives in that file up to, but not including the loading of genprintval.cmo . Please do not change the order of the load directives! It took about half an hour to find the right order....

Alternative preparation step
On the discussion thread, Jonathan Roewen suggested an alternative. It requires rebuilding of the toplevel; the OCaml distribution is no longer needed then. We need to skip the expunge step after the toplevel is built: grep for expunge in the base Makefile. That step erases the mentioning of many internal components from toplevel's module dictionary. Therefore, these OCaml system modules act as if they are not loaded. We need these module for the present application however.

Non-deterministic choice amb

The amb operator, first introduced by John
McCarthy and well described by Dorai Sitaram in the context of Scheme,
takes zero or more expressions (thunks) and nondeterministically
returns the value of one of them. This implies that at least one of amb's expressions must yield a value, that is, does not
fail. If amb has no expressions to evaluate or all of
them fail, amb itself fails. One may think that amb is easily
implementable by taking a list of thunks and
evaluating the thunks in some order within the try
block. The value of the thunk finishing without raising an exception
is returned. However, that simple implementation is wrong. It is not
enough that amb's chosen expression itself evaluates
successfully. The chosen expression must be such that its value causes
the whole program finish without errors, if at all
possible. The amb operator must `anticipate' how the
value of the chosen expression will be used in the rest of the
computation. Therefore, amb is called an angelic
nondeterministic choice operator.

This program, he explained, should return 7: ``the amb
inside the conditional should "know" (be told by an angel) that the
right choice is the second element of the list because it leads to 7,
whereas choosing the first one leads to failure.''

Therefore, we need the ability to examine (or speculatively
execute) the rest of the computation. In Scheme, amb is
implementable in terms of call/cc, as well explained by
Dorai Sitaram. OCaml has more appropriate delimited control operators,
which implement amb in two lines of code. We also need a `toplevel
function', to tell us if the overall computation succeeded. One may
think of it as St. Peter at the gate. For now, we take a computation
that raises no exception as successful. In general, even
non-termination within a branch can be dealt with
intelligently (cf. `cooperative' threading which must yield from time to time).
Andrej Bauer's test now looks in full as

Speculatively evaluating amb's expressions or the rest of the
computation may incur effects, such as mutation or IO. We can deal
with them using one of the standard transaction implementation
techniques: prohibit effects, log the updates, log the state at
the beginning to roll back to, use zipper for functional `mutations'.

Here is a more advanced test, requiring a three-step-ahead clairvoyance
from amb:

In monadic terms, amb is equivalent to msum
in MonadPlus. Even though we are interested in the first
result of the entire MonadPlus computation, along the way
we have to keep track of many possible worlds. That is, we need
something like a List monad rather than a Maybe monad
(the latter should not even be regarded as MonadPlus).

At first sight, that SML feature seems impossible in OCaml (prior to
OCaml 3.12). Although we can declare local exceptions in OCaml via
local structures, before OCaml 3.12 we could not use type variables
quantified outside the structure: a structure limits the scope of all
of its type variables. We show that local globally-quantified
exceptions are macro-expressible in all versions of OCaml and
demonstrate two translations. The first one relies on multi-prompt
delimited continuations, whose implementation leads to the second
translation. The latter represents a polymorphic exception mere by a
parameter-less exception and one reference cell.

The caml-list thread referenced below gave a good motivation
for locally polymorphic exceptions: writing an efficient library
function fold_file of the following interface:

The loop is properly tail-recursive (NB: the body of a try block is not in a tail position) and avoids
any administrative data structures. Alas, the typechecker does not
accept the exception declaration, which says that Done
should carry a value of all types. There is no such value in OCaml,
and if it were, it wouldn't be useful. That was not our intention
anyway: we want the value of Done to have the same type as
the result of the polymorphic function fold_file. We should have
declared the exception insidefold_file. Surprisingly, that can be done: Delimcc.prompt is precisely this type of `local
exceptions'. We need only a slight and local adjustment to the above
code to make it compile. This is our first translation.

The analogy between exceptions and delimited continuations is
profound: local exceptions are commonly used to implement multi-prompt
delimited continuations in SML. We see the converse is
also true. Furthermore, delimited continuations in OCaml are implemented in
terms of exceptions. Abort is essentially raise. If we `inline' the
gist of the delimited continuation library we arrive at our second
translation. The result requires no libraries and works with both
byte-code and native compiler.

The code is still properly tail-recursive and deforested. In
contrast to other imperative implementations of fold_file, ours is
almost pure: the reference cell result is written to
and immediately after read from only once during the whole folding
-- namely, at the very end. The bulk of the iteration is functional.
A mutable cell is the trick behind typing of
multi-prompt delimited continuations. One may even say that if a type
system supports reference cells, it shall support multi-prompt
delimited continuations -- and vice versa.

Version

The current version is 1.2, Oct 4, 2007.

References

Yin-so Chen, Olivier Roussel, kirillkh, et al. best and fastest way to read lines from a file? Caml-list discussion thread. October 1-2, 2007.

Caml-list discussion thread Locally-polymorphic exceptions October 3-4, 2007.
Of special note is the PML implementation posted by Christophe Raffalli.

Type-directed memoization

Memoization of a function is recording and reusing already computed
associations between the argument and the result of the function. The
associations are recorded in a memo table, which can be constructed
generically, with the type determined automatically from the type of
function's argument. The paper ``Fun with type functions'' (Sections
3.1 and 3.2) describes one such generic construction in Haskell, using type
functions, and refers to other constructions. Essentially the same
approach leads to generic finite maps, see Section 3.3 of the paper.

We implement the type-directed memoization from the paper in OCaml.
Quite a few adjustments had to be made. First of all,
OCaml does not have type families, or even type classes. We use
type-indexed--value approach pioneered by Zhe Yang. Second, whereas
Haskell relied on laziness, we explicitly use reference cells for
recording the computed results. Finally, recursive types require an
additional level of indirection via the reference cell. The trick is
not unlike the eta-expansion that converts the ordinary fixpoint
combinator to the applicative one: We have to delay the computation of
the fixpoint until we receive the argument for the fixpointed
function. Still, the computed fixpoint should be shared among all
applications of the memoized function.

Here is a simple example: memoizing functions on boolean lists. A boolean
list has a recursive type (recursive sum of product),
which can be written as:

The type expression for the type of BLST, (unit,bool*'self) either
matches the mathematical notation. Mainly, the expression md_sum md_unit (md_prod md_bool self)
that computes the memoizer for the functions on boolean lists
from the memoizers for unit, booleans and memoizer combinators, too,
matches the mathematical notation for the recursive type of
boolean lists. Our memo tables are indeed type-directed.

Generic print function

The facility that prints results and types of expressions
evaluated at the top-level was available anywhere in the program --
in bytecode- or natively compiled programs. Generic printing is a,
perhaps unintentional, `side-effect' of the old (pre N100) MetaOCaml
-- of the fact that
a code value is not merely AST; the code value also captures the type
and the type environment of variables and other values.

val fprint : Format.formatter -> ('a,'b) code -> string

is the core function which takes a code value of any type, and
pretty-prints it on the given formatter. The printed result is
exactly the same as that by the top-level value printing. The
function fprint returns the representation of the
expression's type, as a string. The latter is arguably a frill, but it
was easy to do, so just as well.

The first line is the value, and the latter (printed by pr_type)
is the type. There was no need to define any custom printer for the
value or its components. A more involved example is given at the end
of the announcement article referenced below.